Page 166 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 105

2
3
2
L M/L L / T

T = [] k [M/LT ] [] L
reveals that

2
[k] = [L ]

2
2
Thus the unit of permeability should be the cm in cgs units, or the metre in Sl units.
Both these units are impracticably large for the majority of reservoir rock, as will be
demonstrated in exercise 4.1, and therefore, a set of units was devised in which the
permeability would have a more convenient numerical size. These are the so-called
"Darcy units" (refer table 4.1) in which the unit of permeability is the Darcy. The latter
was defined from the statement of Darcy's law for horizontal, linear flow of an
incompressible fluid

k dp
u =− (4.11)
µ dl

such that k = 1 Darcy when u = 1 cm/sec; µ = 1 cp; and dp/dl = 1 atmosphere/cm.

Inspection of table 4.1 reveals that the units are a hybrid system based on the cgs
units. The only difference being that pressure is expressed in atmospheres, viscosity in
cp (centipoise) and, as a consequence, the permeability in Darcies. It was intended, in
defining this system of units, that not only would the unit of permeability have a
reasonable numerical value but also, equations expressed in these units would have
the same form as equations in absolute units. That is, there would be no awkward
constants involved in the equations other than multiples of π which reflect the geometry
of the system. Unfortunately, this latter expectation is not always fulfilled because the
Darcy, defined through the use of equ. (4.11), is based on an incomplete statement of
Darcy's law. Certainly, equ. (4.11) has the same form whether expressed in absolute or
Darcy units but considering the general statement of the flow law, equ. (4.9), applied to
an incompressible fluid (ρ ≈ constant), then